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In the presence of sharp (zero radius) V-shaped notches the notch stress intensity factors (N-SIFs) quantify the intensities of the asymptotic linear elastic stress distributions. They are proportional to the limit of the mode I or II stress components multiplied by the distance powered 1 À k i from the notch tip, k i being WilliamsÕ eigenvalues. When the notch tip radius is different from zero, the definition is no longer valid from a theoretical point of view and the characteristic, singular, sharp-notch field diverges from the rounded-notch solution very next to the notch. Nevertheless, NSIFs continue to be used as parameters governing fracture if the notch root radius is sufficiently small with respect to the notch depth.Taking advantage of a recent analytical formulation able to describe stress distributions ahead of rounded Vnotches, the paper gives a generalized form for the notch stress intensity factors, in which not only the opening angle but also the tip radius dimension is explicitly involved. Such parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case.

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Analytical solutions are developed for the stress fields induced by circumferential U- and blunt V-shaped notches in axisymmetric shafts under torsion, with a finite value of the notch root radius. The boundary value problem is formulated by using complex potential functions and the real boundary notch shape. Shear stress components are then written as a function of the maximum shear stress evaluated at the notch tip. Considering different global and local geometries the obtained equations are compared with a large bulk of finite element results, showing a very good agreement. Due to their reduced complexity, such equations turn out to be particularly useful in practice

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